Abstract

Since the topic of sliding mode control was introduced to the international control community following early pioneering work in the former Soviet Union in the 1960’s, the methodology has stimulated the development of theoretical work that has impacted on both theory and practice. Fundamental to the approach is its total invariance to an important class of parameter variations and uncertainty. A further advantage is that the dynamic behaviour of the system may be directly tailored by the choice of a so-called switching function – essentially this switching function can be thought of as a measure of the desired performance. This presentation will first review the basic properties and terminology of classical, sometimes called first order sliding mode control. The robustness of the sliding mode control methodology is due to the so called principle of the equivalent injection, whereby the average value of the applied control signal reconstructs the uncertainty. This property facilitates the development of sliding mode observers which force the error between the measured plant output and the output of the observer to be identically zero. The observer produces a set of state estimates that are precisely commensurate with the actual output of the plant and the corresponding equivalent injection signal contains useful information about the mismatch between the model used to define the observer and the actual plant. The lecture will introduce the sliding mode observer paradigm and results will be presented showing how the ideas can be used to develop Anti-Lock Braking Systems (ABSs) for next generation electric vehicles. Here the disruptive effect of the introduction of electric vehicles has stimulated industry to completely revisit established designs and supply chains. The so called higher-order sliding mode control paradigm will then be introduced. This method was motivated by a desire to ensure finite-time convergence in the presence of uncertainty via a smooth control. This is achieved by ensuring the discontinuous control action acts directly on higher order derivatives of the switching function. The concept of higher order sliding mode control has stimulated strong theoretical results in the area of robust, exact differentiation of signals. The presentation will conclude by introducing a sliding mode differentiator toolbox which has been developed in collaboration with colleagues from TU Graz.